Extra Ch. 1 Problems
1)
Do Problem 3 on p. 15 of Ross.
Express answer by giving both an exact expression and using scientific notation, rounding to
three significant digits. (E.g., if the exact answer to a problem could be expressed as the binomial coefficient
50 choose 25 (so equal to 50!/[(25!)(25!)]), then the answer in scientific notation would be 1.26 × 1014.)
You don't need to show any work or provide any explanation.
2)
Do part (d) of Problem 8 on p. 16 of Ross, ignoring the fact that the first letter is capitalized, and ignoring the
question mark. (So how many distinct arrangements of the letters in arrange are there?)
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.
3)
Do part (a) of Problem 14 on p. 16 of Ross, only change the class size from 30 to 20.
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.
4)
Do part (b) of Problem 14 on p. 16 of Ross, only change the class size from 30 to 20.
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.
5)
Do Problem 15 on p. 16 of Ross, only change the group size from 20 to 10.
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.
6)
Do part (a) of Problem 18 on p. 16 of Ross, only change the number of math books from 6 to 16 (since 6 is just too few math books).
Express your final answer as an integer, but also show some work and provide a brief written explanation to indicate
how you arrived at your final answer.
7)
Do part (a) of Problem 22 on p. 16 of Ross, only change the number of friends from 8 to 18 (since it's just too sad to consider
a person with only 8 friends).
Express your final answer as an integer, but also show some work and provide a brief written explanation to indicate
how you arrived at your final answer.
8)
Answer the first question of Problem 34 on p. 17 of Ross, only change the number of blackboards from 8 to 9.
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.
(Note: In this problem the schools are distinguishable, but the blackboards aren't. This is different from Problem 31 on p. 17
of Ross in which both the teachers and the schools are distinguishable.)
9)
Answer the second question of Problem 34 on p. 17 of Ross, only change the number of blackboards from 8 to 9.
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.
10)
Do Exercise 2 on p. 18 of Ross.
You don't need to show any work or provide any explanation.
11)
Do Problem 19 on p. 16 of Ross.
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.
12)
Do Problem 23 on pp. 16-17 of Ross.
Express your final answer as an integer, but also show some work and provide a brief written explanation to indicate
how you arrived at your final answer.
13)
Do Problem 24 on p. 17 of Ross.
Express your final answer as an integer, but also show some work and provide a brief written explanation to indicate
how you arrived at your final answer.
14)
Do Problem 28 on p. 17 of Ross.
Give an exact expression for your answer (possibly including factorials, binomial coefficients, or multinomial coefficents),
and also express your answer numerically using scientific notation, rounding to three significant digits.
(Note: To clarify what is being asked for, we want how many ways a dealer can deal the deck of 52 cards to three other players and himself,
giving 13 of the cards to each person.)
15)
Answer the first question of Problem 31 on p. 17 of Ross.
(Note: Both the teachers and the schools are distinguishable, unlike in Problem 34 where the schools are distinguishable
but the blackboards aren't.)
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.
16)
Answer the second question of Problem 31 on p. 17 of Ross.
(Note: Both the teachers and the schools are distinguishable, unlike in Problem 31 where the schools are distinguishable
but the blackboards aren't.)
While you don't need to show a lot of work or provide any written explanation, I want you to give an
expression which indicates where your final answer, expressed as an integer, comes from.